derivative of (2-x/(x^2+4))

解

\frac{d}{d x} (\frac{2 - x}{x ^{2} + 4})

\frac{x ^{2} - 4 x - 4}{( x ^{2} + 4 ) ^{2}}

解答ステップ

\frac{d}{d x} (\frac{2 - x}{x ^{2} + 4})

商の法則を適用:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( 2 - x ) ( x ^{2} + 4 ) - \frac{d}{d x} ( x ^{2} + 4 ) ( 2 - x )}{( x ^{2} + 4 ) ^{2}}

\frac{d}{d x} (2 - x) = - 1

\frac{d}{d x} (x^{2} + 4) = 2 x

= \frac{( - 1 ) ( x ^{2} + 4 ) - 2 x ( 2 - x )}{( x ^{2} + 4 ) ^{2}}

簡素化

\frac{( - 1 ) ( x ^{2} + 4 ) - 2 x ( 2 - x )}{( x ^{2} + 4 ) ^{2}} : \frac{x ^{2} - 4 x - 4}{( x ^{2} + 4 ) ^{2}}

= \frac{x ^{2} - 4 x - 4}{( x ^{2} + 4 ) ^{2}}